Question

On a certain map, every 2 cm represents 10 km on Earth's surfaceWhich ratio represents the scale of the map, which shows how the map measurements compare to actual ones on Earth's surface?

Answer 1

So, the ratio that represents the scale of the map is 1 : 500.000 or 1 cm on the map is equal to 5 km in the actual disctance on Earth's surface..

Introduction and Formula Used

Hi! Here I will help you to solve problems related to the relationship between distance that represent on the map and the actual distance on Earth's surface. For this problem, we can convert a unit that same as the other or convert both to the nearest SI unit. For example, in this case the distances on the map in cm unit and actual distances in km unit, we can convert both unit into cm unit. Or, you have another option by converting cm and km units to SI units, namely m unit. For that conversion in distance remember that:

`\begin{array}l\underline{km~}\\~~~~\underlinehm\\~~~~~~~~~~\underlinedam~~~~~~~~\\warrow/10\\~~~~~~~~~~~~~~~~\underline\\~~~~~~~~~~\searrow~~~~~\underline\\~~*10~~~~~~~~~~~~~~~~\underline\\\underline~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\end{array}\\~~~~~~~~~~~\rm Distance~Unit`

With the following condition:

• If we converting a unit from km to hm and below, each the units go downstair times by 10
• If we converting a unit from km to hm and below, each the units go upstair divided by 10

Then, the formula to count the ratio that represent how the map compare to actual ones on Earth's surface can be expressed by this equation:

`\boxed{\sf{\bold{map \: scale = (map \: distance)/(actual \: distance)}}}`

Problem Solving

We know that:

• map distance = 2 cm
• actual distance = 10 km =
  `\sf{10 * 100.000}` = 1.000.000 cm

What was asked?

• map scale = ... ?

Step by step:

`\sf{\bold{map \: scale = (map \: distance)/(actual \: distance)}}`

`\sf{map \: scale = (2)/(1.000.000)}`

`\sf{map \: scale = (1)/(500.000)}`

Conclusion

So, the ratio that represents the scale of the map is 1 : 500.000 or 1 cm on the map is equal to 5 km in the actual disctance on Earth's surface.